A Note on Weakly Semiprime Ideals and Their Relationship to Prime Radical in Noncommutative Rings

IF 1.3 4区数学 Q1 MATHEMATICS Journal of Mathematics Pub Date : 2024-05-24 DOI:10.1155/2024/9142090

Alaa Abouhalaka

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Abstract

In this paper, we introduce the concept of weakly semiprime ideals and weakly -systems in noncommutative rings. We establish the equivalence between an ideal being a weakly semiprime ideal and being a weakly -system. We provide alternative definitions and explore the properties of weakly semiprime ideals. Additionally, we investigate scenarios where all ideals in a given ring are weakly semiprime and demonstrate that in Noetherian rings, where every ideal is weakly semiprime, the prime radical and the Jacobson radical coincide.

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关于非交换环中的弱半素数理想及其与素根的关系的说明

本文介绍了非交换环中弱半理想和弱-系统的概念。我们建立了弱半枚举理想与弱-系统之间的等价关系。我们提供了弱半整数理想的替代定义，并探讨了弱半整数理想的性质。此外，我们还研究了给定环中所有理想都是弱半枚举的情况，并证明在诺特环中，每个理想都是弱半枚举，质根和雅各布森根重合。

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来源期刊

Journal of Mathematics Mathematics-General Mathematics

CiteScore

2.50

自引率

14.30%

发文量

期刊介绍： Journal of Mathematics is a broad scope journal that publishes original research articles as well as review articles on all aspects of both pure and applied mathematics. As well as original research, Journal of Mathematics also publishes focused review articles that assess the state of the art, and identify upcoming challenges and promising solutions for the community.